Mathematica > Mathematics and Algorithms > Discrete Mathematics > Group Theory > Named Groups > SymmetricGroup
BUILT-IN MATHEMATICA SYMBOL

SymmetricGroup

SymmetricGroup[n]
represents the symmetric group of degree n.

DetailsDetails

  • The degree n of SymmetricGroup[n] must be a non-negative integer. Degrees 0 and 1 correspond to the trivial or identity group.
  • SymmetricGroup[n] is represented by default as a permutation group on the points .

ExamplesExamplesopen allclose all

Basic Examples (3)Basic Examples (3)

Number of elements of a symmetric group:

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Permutation generators of a symmetric group:

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Elements of a permutation representation of a symmetric group:

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Scope (1)Scope (1)

Applications (1)Applications (1)

Properties & Relations (1)Properties & Relations (1)

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